Part One – Set notation and problem solving with Venn …



00006187440000The Essington International School DarwinYear 8 MathematicsNameClassAssignment TitleVenn Diagrams and SetsDate GivenDue DateExtension RequiredYES NODescription of Assessment TaskPart 1: Represent all whole numbers from 1 to 30 in a Venn Diagram and use this representation to solve a problem. Show this data with set notationPart 2: Create a Venn diagram that accurately represents data from categoriesPart 3: Solve a ‘sharing’ problem with a variety of solutions using Venn diagramsPresentation Follow the investigation steps listed on the following pages the task sheet to produce a comprehensive representation of how to use Venn diagrams. Your report should include any relevant explanations or working that is needed to explain your results Your final report will include: Part 1: Two Venn diagrams, a table of Set notation and the answer to a problem.Part 2: One Venn diagram of categorised dataPart 3: Various Venn diagram solutions to an open ended problemTime AllocationYou will be given 2 lessons per week during Term 2 Week 1, 2 and, 3 to work on your assignment. The assignment will also be included in your homework over this period.Learning Intentions/Student Checklist Use Venn diagrams to solve a problemUse set notationRepresent data with the use of a Venn diagramDemonstrate understanding of variable solutions to problemsGradeCommentContentABCDEVenn Diagrams 50%Constructs a comprehensive range of Venn diagrams to represent data and solve problems. Constructs a range of Venn diagrams to represent data and solve problems. Constructs valid Venn diagrams to represent data.Constructs Venn diagrams in scaffolded situations. Displays some Venn diagrams.Procedures and Mathematical Notation and Terminology20%Investigation procedure demonstrates a thorough understanding and use of Venn diagrams. Correct terminology and set notation are always used, making it easy to understand what was done.Investigation procedure mostly demonstrates a good understanding of use of Venn diagrams. Correct terminology and set notation are usually used, making it fairly easy to understand what was done.Investigation procedure demonstrates a sound understanding of use of Venn diagrams. Correct terminology and set notation are used, but it is sometimes not easy to understand what was done.Investigation procedure shows little understanding of use of Venn diagrams.There is little use, or a lot of inappropriate use, of terminology and set notation.Investigation shows no understanding of use of Venn diagrams. No use of terminology or set notation.Analysis and Solutions20%Analysis and conclusions consider the full range of available solutions to each problem. Uses complex and refined mathematical reasoning. Explanation is clear and detailed.Analysis and conclusions consider a wide range of available solutions to each problem. Uses effective mathematical reasoning. Explanation is clear.Analysis draws on some solutions to each problem, but conclusions lack depth and detail. Some evidence of mathematical reasoning. Explanation is clear.Draws conclusions based on isolated solutions to problems. Little evidence of mathematical reasoning. Solution is difficult to understand and is missing several components.Provides loosely linked reasons for conclusions. There is no evidence of mathematical reasoning. Explanation is not evident or it has not been included.Presentation 10%The work is presented in a neat, clear, organized fashion that is easy to read. The work is presented in a neat and organized fashion that is usually easy to read. The work is presented in an organized fashion but may be hard to read at times. The work appears disordered. It is hard to know what information goes together.The work is very disordered. Sections are missing and it is very difficult to know what information goes together.Part One – Set notation and problem solving with Venn diagramsComplete the Venn diagram below for the integers 1 to 30. The two sections being ‘multiples of 2’ and ‘multiples of 5’.Similarly to above, use technology to create your own Venn diagram for the integers 1 to 30, with the three sections being ‘multiples of 2’, ‘multiples of 3’ and ‘multiples of 5’.Complete the following tableCategoryNumber of elements (out of 30)Set notationMultiple of 2Multiple of 3Multiple of 5Not a multiple of 2Not a multiple of 3Not a multiple of 5Multiple of 2, but not 3 or 5Multiple of 3, but not 2 or 5Multiple of 5, but not 2 or 3Multiple of 2 or 3Multiple of 2 or 5Multiple of 3 or 5Multiple of 2 and 3, but not 5Multiple of 2 and 5, but not 3Multiple of 3 and 5, but not 2Multiple of 2 and 3 and 5Not a multiple of 2, 3 or 5Based on your findings from part b, how many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5? When you have an answer include a brief statement (a sentence or two) or some appropriate working out to show how you figured it out.Optional: Repeat this question, replacing at least one of the primes (2, 3, 5) with another prime.Part Two – Venn diagrams to represent and categorise dataChoose 3 categories that are not mutually exclusive.Create a Venn diagram that has as many elements as possible in each section.Make sure that Each section has something in itEach element you include is in the correct sectionSome examples of categories could beSweet, salty, sour (food)or you could swap one out for ‘spicy’Protein, carbs, fats (foods)physical, outdoors, with a group (activities)solo artist, in a band, plays an instrument (musicians)Has legs, is a good swimmer, hatches from an egg (animals)From DC Universe, from Marvel universe, never been in a movieAsk your teacher for more examples if you get stuckPart Three – Birthday Plants 1: Venn diagrams for variable solutionsOn their next Birthdays, Naomi will be 5, Alex will be 6 and Chris will be 7. All three children will be given some plants for the garden, one for each year they have been alive. That is, Naomi will be given 5 plants, Alex will be given 6 and Chris will be given 7.Here is the plan of their house and garden:Each child is to have a circle to grow their trees in but there will be some bits that are shared, around the middle.The family has decided they can only afford 10 plants in total.The children do not believe it is possible for them to each have 5, 6 and 7 plants in their circles and have this add up to only 10 plants in total.See if you can help them. Here is the taskFind as many solutions as you can to the following problem:Use exactly 10 plants (no more, no less)The circles must contain 5, 6, and 7 plants exactly.Use the sheet over the page to record your results.Create a table of Set notation for one of the solutions.Birthday Plants 2 (Optional): Complex Venn diagrams for variable solutionsAttempt to create overlapping sections for the following situationsFour overlapping shapes (1)Draw the four shapes so that there is a section for each sharing situation.Allocate 4, 5, 6, and 7 plants to each of the areasUse a total of 19 plants onlyFour overlapping shapes (2)Draw the four shapes so that there is a section for each sharing situation.Allocate 3, 4, 5, and 6 plants to each of the areasUse a total of 15 plants onlyFive overlapping shapes (1)Draw the five shapes so that there is a section for each sharing situation.Allocate 1, 4, 5, 6, and 7 plants to each of the areasUse a total of 19 plants onlyFive overlapping shapes (2)Draw the five shapes so that there is a section for each sharing situation.Allocate 1, 3, 4, 5, and 6 plants to each of the areasUse a total of 15 plants onlyAsk your teacher for assistance if you cannot think of how to design the overlapping areas.Ask your teacher for another copy of this page if you need one ................
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